/*
 * CXSPARSE: a Concise Sparse Matrix package - Extended.
 * Copyright (c) 2006-2009, Timothy A. Davis.
 * http://www.cise.ufl.edu/research/sparse/CXSparse
 * 
 * CXSparse is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 * 
 * CXSparse is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public
 * License along with this Module; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 */

#include "cs.h"
/* L = chol (A, [pinv parent cp]), pinv is optional */
csn *cs_chol (const cs *A, const css *S)
{
    CS_ENTRY d, lki, *Lx, *x, *Cx ;
    CS_INT top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ;
    cs *L, *C, *E ;
    csn *N ;
    if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ;
    n = A->n ;
    N = cs_calloc (1, sizeof (csn)) ;       /* allocate result */
    c = cs_malloc (2*n, sizeof (CS_INT)) ;     /* get CS_INT workspace */
    x = cs_malloc (n, sizeof (CS_ENTRY)) ;    /* get CS_ENTRY workspace */
    cp = S->cp ; pinv = S->pinv ; parent = S->parent ;
    C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ;
    E = pinv ? C : NULL ;           /* E is alias for A, or a copy E=A(p,p) */
    if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ;
    s = c + n ;
    Cp = C->p ; Ci = C->i ; Cx = C->x ;
    N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ;    /* allocate result */
    if (!L) return (cs_ndone (N, E, c, x, 0)) ;
    Lp = L->p ; Li = L->i ; Lx = L->x ;
    for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ;
    for (k = 0 ; k < n ; k++)       /* compute L(k,:) for L*L' = C */
    {
        /* --- Nonzero pattern of L(k,:) ------------------------------------ */
        top = cs_ereach (C, k, parent, s, c) ;      /* find pattern of L(k,:) */
        x [k] = 0 ;                                 /* x (0:k) is now zero */
        for (p = Cp [k] ; p < Cp [k+1] ; p++)       /* x = full(triu(C(:,k))) */
        {
            if (Ci [p] <= k) x [Ci [p]] = Cx [p] ;
        }
        d = x [k] ;                     /* d = C(k,k) */
        x [k] = 0 ;                     /* clear x for k+1st iteration */
        /* --- Triangular solve --------------------------------------------- */
        for ( ; top < n ; top++)    /* solve L(0:k-1,0:k-1) * x = C(:,k) */
        {
            i = s [top] ;               /* s [top..n-1] is pattern of L(k,:) */
            lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */
            x [i] = 0 ;                 /* clear x for k+1st iteration */
            for (p = Lp [i] + 1 ; p < c [i] ; p++)
            {
                x [Li [p]] -= Lx [p] * lki ;
            }
            d -= lki * CS_CONJ (lki) ;            /* d = d - L(k,i)*L(k,i) */
            p = c [i]++ ;
            Li [p] = k ;                /* store L(k,i) in column i */
            Lx [p] = CS_CONJ (lki) ;
        }
        /* --- Compute L(k,k) ----------------------------------------------- */
        if (CS_REAL (d) <= 0 || CS_IMAG (d) != 0)
	    return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */
        p = c [k]++ ;
        Li [p] = k ;                /* store L(k,k) = sqrt (d) in column k */
        Lx [p] = sqrt (d) ;
    }
    Lp [n] = cp [n] ;               /* finalize L */
    return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */
}